Problem: $\dfrac{1}{9} \div \dfrac{8}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{8}{9}$ is $\dfrac{9}{8}$ Therefore: $ \dfrac{1}{9} \div \dfrac{8}{9} = \dfrac{1}{9} \times \dfrac{9}{8} $ $ \phantom{\dfrac{1}{9} \times \dfrac{9}{8}} = \dfrac{1 \times 9}{9 \times 8} $ $ \phantom{\dfrac{1}{9} \times \dfrac{9}{8}} = \dfrac{9}{72} $